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 2d revised Proving $\frac{1}{c} = \frac{1}{a} + \frac{1}{b}$ in a geometric context added 39 characters in body 2d answered Proving $\frac{1}{c} = \frac{1}{a} + \frac{1}{b}$ in a geometric context 2d answered Why $-1 \leq\frac{\langle A,B\rangle}{||A||\, ||B||}\leq1$? Apr12 comment Set of points at which a function coincides with its convexification is compact? Yes, I guess lower semicontinuous could work. Apr12 answered Set of points at which a function coincides with its convexification is compact? Apr12 answered $x\over(1-x)$ $y\over(1-y)$ $z\over(1-z)$ >= 8 when $x ,y ,z$ are positive proper fractions and $x+y+z = 2$ Apr12 comment $x\over(1-x)$ $y\over(1-y)$ $z\over(1-z)$ >= 8 when $x ,y ,z$ are positive proper fractions and $x+y+z = 2$ What does proper fractions mean? Are they rational numbers? Apr11 comment Proving properties about matrix $A$ s.t. $A^2 = -I$ The equation you get for $\lambda$ is $\lambda^2 = -1$. This has roots $\pm i$. The sum of the eigenvalues is equal to the trace (the sum of the elements on the diagonal), and since $A$ has real entries, the trace is real. Apr11 answered For $n \ge 3$, every subgroup of $A_n$ with index $n$, is isomorphic to $A_{n-1}$ Apr11 comment For $n \ge 3$, every subgroup of $A_n$ with index $n$, is isomorphic to $A_{n-1}$ I guess you could use the fact that for $n \geq 5$, normal subgroups of $S_n$ are $\{e\},A_n,S_n$. Prove that a subgroup of $A_n$ with index $n$ is a normal subgroup of a group isomorphic to $S_{n-1}$. Then its cardinality implies that it can only be $A_{n-1}$. Apr11 answered Proving the series doesn't converge: $\sum_{n=1}^{\infty}a_n$, $\lim_{n\to\infty}na_n=\infty$, $a_1=-1$ Apr11 answered To find the value of a function at a point where it is continuous Apr11 awarded linear-algebra Apr10 comment Learning modern differential geometry before curves and surfaces I don't see why what you are doing could not be "safe". But it's just like talking about derivatives, without actually finding a derivative of a concrete function like $\exp,\sin,\ln$. Differential geometry was not a success for me, and as I look back, is this lack of concrete examples and connection with the curves and surfaces which kept me from learning more. I liked this course on curves and surfaces: alpha.math.uga.edu/~shifrin/ShifrinDiffGeo.pdf If you like differential geometry, you'll like curves and surfaces. Apr10 answered Proving properties about matrix $A$ s.t. $A^2 = -I$ Apr10 comment Learning modern differential geometry before curves and surfaces If you're comfortable with geometry on manifolds, it costs nothing to take a look into curves and surfaces. How can you speak of the tangent space to a manifold without being able to work with tangents to curves, or tangent planes to surfaces? How do you compute the curvature of a curve, or the mean curvature of a surface at a point? These are basic questions you need to know from curves and surfaces... Apr10 revised Equal-area sparse spherical shell partitioning added 87 characters in body Apr9 comment Please help solve for the variables A and B Replace B in the first equation. Then you'll have just an equation in A Apr9 comment Find all functions $f$ such that if $a+b$ is a square, then $f(a)+f(b)$ is a square @Elaqqad: The article you cite proves this only for polynomials, as far as I see. Apr9 revised Unique solution of nolinear equation set added 124 characters in body